SOLUTION: apply the quadratic formula to find the roots of the given function, and then graph the function. f(x) = x2 - 4

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: apply the quadratic formula to find the roots of the given function, and then graph the function. f(x) = x2 - 4      Log On


   

Question 48344: apply the quadratic formula to find the roots of the given function, and then graph the function.
f(x) = x2 - 4
Found 2 solutions by stanbon, venugopalramana:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
f(x) = x^2 - 4
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B0x%2B-4+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%280%29%5E2-4%2A1%2A-4=16.

Discriminant d=16 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-0%2B-sqrt%28+16+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%280%29%2Bsqrt%28+16+%29%29%2F2%5C1+=+2
x%5B2%5D+=+%28-%280%29-sqrt%28+16+%29%29%2F2%5C1+=+-2

Quadratic expression 1x%5E2%2B0x%2B-4 can be factored:
1x%5E2%2B0x%2B-4+=+1%28x-2%29%2A%28x--2%29
Again, the answer is: 2, -2. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B0%2Ax%2B-4+%29

Cheers,
Stan H.

Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
apply the quadratic formula to find the roots of the given function, and then graph the function.
f(x) = x2 - 4=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-0+%2B-+sqrt%28+0%5E2-4%2A1%2A%28-4%29+%29%29%2F%282%2A1%29+
x+=+%280+%2B-+sqrt%28+16+%29%29%2F%282%29+
x+=+%280+%2B-+4%29%2F%282%29+
X=2..OR...-2
X.....0.......1......2.......3........4.....ETC
Y.....-4......-3.....0.......5........12
+graph%28+500%2C+500%2C+-5%2C+5%2C+-10%2C+10%2C+x%5E2-4%29+